Will Factoring solve the problem?

Algebra Level 3

(x+1x)6(x6+1x6)2(x+1x)3+(x3+1x3)\frac{{\left(x+\dfrac{1}{x}\right)}^6-\left(x^6+\dfrac{1}{x^6}\right)-2}{{\left(x+\dfrac{1}{x}\right)}^3+\left(x^3+\dfrac{1}{x^3}\right)}

If xx is a positive real number, then find the minimum value of the expression above.

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